The integral homology of PSL(2) of imaginary quadratic integers with nontrivial class group

We show that a cellular complex defined by Flöge allows us to determine the integral homology of the Bianchi groups PSL(2)(O[-m]), where O[-m] is the ring of integers of an imaginary quadratic number field Q [square root -m] for a square-free natural number m. In the cases of nontrivial class group, we handle the difficulties arising from the cusps associated to the nontrivial ideal classes of O(-m). We use this to compute the integral homology of PSL(2)(O[-m]) in the cases m=5,6,10,13 and 15, which previously was known only in the cases m=1,2,3,7 and 11 with trivial class group.